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91.
Ionel Sorinel Ciuperca 《Journal of Dynamics and Differential Equations》1998,10(1):73-108
We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain. 相似文献
92.
《Mathematische Nachrichten》2017,290(1):37-49
We prove that Burenkov's extension operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n‐dimensional Euclidean space. 相似文献
93.
Well‐posedness and regularity results for a 2m‐th order parabolic equation in symmetric conical domains of ℝN+1
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Saïda Cherfaoui Amor Kessab Arezki Kheloufi 《Mathematical Methods in the Applied Sciences》2017,40(16):6035-6047
In this paper, we use the domain decomposition method to prove well‐posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high‐order parabolic equation set in conical time‐dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
94.
For the most part, analytical solutions for steady unsaturated infiltration have been restricted to infinite and semi-infinite seepage geometries, using the quasi-linear approximation for the hydraulic conductivity. We provide analytical series methods to solve the steady quasi-linear flow equations, in finite irregular seepage geometries. Unlike the classical approach, the series method has been modified, to cater for arbitrary boundary geometry and surface recharge distributions. The matrix flux potential and the stream function both satisfy the same governing partial differential equation, and the stream function formulation is used to estimate the series coefficients. For a finite vadose zone, the stream function solution does not uniquely determine the matrix flux potential, when flux boundary conditions are used. Consequently, the stream function solution applies to a range of moisture distributions, for given infiltration and evapotranspiration rates through the surface. 相似文献
95.
A. A. Shutov 《Fluid Dynamics》2006,41(6):901-915
The shape of a charged jet is determined in the approximation of a strong electric field. The stability of the jet with respect to both axisymmetric and nonaxisymmetric perturbations of the sinusoidal type is investigated in the linear approximation. The domains of predominance of the axisymmetric and bending modes and the longitudinal partition mode are determined. Experimental data on the longitudinal partition of a polymeric jet into several daughter jets are given. 相似文献
96.
We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a real parameter ? and we denote by u? the corresponding solution. The behavior of u? for ? small and positive can be described in terms of real analytic functions of two variables evaluated at (?,1/log??). We show that under suitable assumptions on the geometry and on the boundary data one can get rid of the logarithmic behavior displayed by u? for ? small and describe u? by real analytic functions of ?. Then it is natural to ask what happens when ? is negative. The case of boundary data depending on ? is also considered. The aim is to study real analytic families of harmonic functions which are not necessarily solutions of a particular boundary value problem. 相似文献
97.
98.
Paolo Zanardo 《代数通讯》2015,43(1):158-173
Let R be a commutative ring and A be an R-module. The Mal'cev rank μ(A) of A is the sup of genN, where N ranges over the finitely generated submodules of A, and genN is the minimum number of generators of N. We prove that μ is both sub-additive and pre-additive as an invariant of Mod(R). Our main goal is to investigate μ for modules over pseudo-valuation domains. Specifically, we establish which pseudo-valuation domains R satisfy the property that an R-module of finite Mal'cev rank must be finitely generated. We split the class 𝒞 of pseudo-valuation domains as a union 𝒞 = 𝒞1 ∪ 𝒞2 ∪ 𝒞3 ∪ 𝒞4 of suitably defined subclasses, and prove that the property holds if and only if R ∈ 𝒞3 ∪ 𝒞4. In that case we can describe the R-modules A where μ(A) < ∞. We also show that, for R ∈ 𝒞4, there exist indecomposable R-modules of arbitrarily large finite Mal'cev rank. 相似文献
99.
In this paper we first show that the total energy of solutions for a semilinear system of elastic waves in Rn with a potential type of damping decays in an algebraic rate to zero. We study the critical potential case and we assume that the initial data have a compact support. An application for the Euler-Poisson-Darboux type dissipation V(t,x) is obtained and in this case the compactness of the support on the initial data is not necessary. Finally, we shall discuss the energy concentration region for the linear system of elastic waves in an exterior domain. 相似文献
100.
Liangliang DuXionghua Wu 《Applied mathematics and computation》2011,218(4):1379-1388
A rational differential quadrature method in irregular domains (RDQMID) is investigated to deal with a kind of singularly perturbed problems with boundary layers. Through a transformation, the boundary layer, which may be not straight, is transformed into a segment of a line parallel to one of the Cartesian axes. The rational differential quadrature method (RDQM) is applied to discretize the governing equation. Finally, a direct expansion method of the boundary conditions (DEMBC) is raised to deal with the boundary conditions. Numerical experiments show that RDQMID is of high accuracy, efficiency and easy to programme. 相似文献